1. Central Tendency

2. Central Tendency
statistical measure that accurately describes the center of the distribution and represents the entire distribution of scores.
a descriptive statistic

3. Measures of Central Tendency80 75 90 95 65 86 97 50
Mean
Median
Mode

4. Median 2 5 8 12 14 15 17 19
Middle value, or 50th percentile

5. Median
When there are several scores with the same value in the middle of the distribution
Use the following formula:
Where:
XLRL= lower real limit of the tied values
fLRL= frequency of scores with values below XLRL
Ftied = frequency for the tied values

6. Example X f 5 1 4 3 2

7. Mode Most frequently occurring score in a data set 2 5 8 12 14 15 1719
Most frequently occurring score in a data set

8. Reporting Central Tendency in Research Reports
In manuscripts and in published research reports, the sample mean is identified with the letter M.
There is no standardized notation for reporting the median or the mode.
In research situations where several means are obtained for different groups or for different treatment conditions, it is common to present all of the means in a single graph.

9. Variability

10. What is Variability?

11. Measuring Variability
the range
the standard deviation/variance.

12. Example

13. Variance and Standard Deviation (SD)
The most commonly used and most important measure of variability
Is the average distance (deviation) between each score in a distribution and the mean of the distribution

14. Example
Score
(X)
Mean
(M)
Deviation
(X-M)
(X-M)2 1 2 3 4

15. Variance Variance = = Sum of the squared deviations = SS
number of scores N
= 5.2 5
= 1.04
For samples, variance is computed by dividing the sum of the squared deviations (SS) by n - 1, rather than N (will provide an unbiased estimate of the population variance)

16. Standard Deviation (SD)
M=2.6
SD=0.55
M=2.6
SD=1.82

17. Computational Formula for SS
Score
(X) 1 2 3 4